Comments on Holographic Complexity - INSPIRE

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Comments on Holographic Complexity

Dean Carmi
(
- Perimeter Inst. Theor. Phys. and
- Tel Aviv U.
)
,
Robert C. Myers
(
- Perimeter Inst. Theor. Phys.
)
,
Pratik Rath
(
- Perimeter Inst. Theor. Phys. and
- UC, Berkeley
)

Dec 1, 2016

41 pages

Published in:

JHEP 03 (2017) 118

Published: Mar 22, 2017

e-Print:

1612.00433 [hep-th]

DOI:

10.1007/JHEP03(2017)118

View in:

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Abstract: (arXiv)

We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

Note:

Minor corrections in section 5

AdS-CFT Correspondence
Classical Theories of Gravity
Gauge-gravity correspondence
holography
geometry
surface

References(67)

Figures(9)

[1]

Quantum Computational Complexity

John Watrous
(
- Waterloo U. and
- Waterloo U., IQC
)

[2]

Quantum hamiltonian complexity

S. Gharibian
,
Y. Huang
,
Z. Landau
,
S.W. Shin

- Theor.Comput.Sci. 10 (2015) 159-282
•
e-Print:
- 1401.3916

[3]

Hamiltonian complexity

Tobias J. Osborne

- Rept.Prog.Phys. 75 (2012) 2, 022001
•
DOI:
- 10.1088/0034-4885/75/2/022001

[5]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[5]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[6]

Complexity and Shock Wave Geometries

Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.D 90 (2014) 12, 126007
•
e-Print:
- 1406.2678
•
DOI:
- 10.1103/PhysRevD.90.126007

[7]

Switchbacks and the Bridge to Nowhere

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

e-Print:
- 1408.2823

[8]

Entanglement is not enough

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 49-71
•
e-Print:
- 1411.0690
•
DOI:
- 10.1002/prop.201500095

[9]

Holographic Complexity Equals Bulk Action?

Adam R. Brown
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, CTP and
- MIT, LNS
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Brian Swingle
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.Lett. 116 (2016) 19, 191301
•
e-Print:
- 1509.07876
•
DOI:
- 10.1103/PhysRevLett.116.191301

[10]

Complexity, action, and black holes

Adam R. Brown
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, CTP and
- MIT, Cambridge, Dept. Phys.
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Brian Swingle
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.D 93 (2016) 8, 086006
•
e-Print:
- 1512.04993
•
DOI:
- 10.1103/PhysRevD.93.086006

[11]

Noether charge, black hole volume, and complexity

Josiah Couch
(
- Texas U. and
- Texas U., TCC
)
,
Willy Fischler
(
- Texas U. and
- Texas U., TCC
)
,
Phuc H. Nguyen
(
- Texas U. and
- Texas U., TCC
)

- JHEP 03 (2017) 119
•
e-Print:
- 1610.02038
•
DOI:
- 10.1007/JHEP03(2017)119

[12]

How big is a black hole?

- Phys.Rev.D 91 (2015) 6, 064046
•
e-Print:
- 1411.2854
•
DOI:
- 10.1103/PhysRevD.91.064046

[13]

Volume inside old black holes

- Phys.Rev.D 94 (2016) 10, 104002
•
e-Print:
- 1604.07222
•
DOI:
- 10.1103/PhysRevD.94.104002

[14]

Gravitational action with null boundaries

- Phys.Rev.D 94 (2016) 8, 084046
•
e-Print:
- 1609.00207
•
DOI:
- 10.1103/PhysRevD.94.084046

[15]

Holographic derivation of entanglement entropy from AdS/CFT

- Phys.Rev.Lett. 96 (2006) 181602
•
e-Print:
- hep-th/0603001
•
DOI:
- 10.1103/PhysRevLett.96.181602

[16]

Aspects of Holographic Entanglement Entropy

Shinsei Ryu
(
- Santa Barbara, KITP
)
,
Tadashi Takayanagi
(
- Kyoto U.
)

- JHEP 08 (2006) 045
•
e-Print:
- hep-th/0605073
•
DOI:
- 10.1088/1126-6708/2006/08/045

[17]

On Holographic Entanglement Entropy and Higher Curvature Gravity

- JHEP 04 (2011) 025
•
e-Print:
- 1101.5813
•
DOI:
- 10.1007/JHEP04(2011)025

[18]

Some Calculable Contributions to Holographic Entanglement Entropy

- JHEP 08 (2011) 039
•
e-Print:
- 1105.6055
•
DOI:
- 10.1007/JHEP08(2011)039

[19]

A Quantum Source of Entropy for Black Holes

- Phys.Rev.D 34 (1986) 373-383
•
DOI:
- 10.1103/PhysRevD.34.373

[20]

Entropy and area

Mark Srednicki
(
- UC, Berkeley, CfPA and
- LBL, Berkeley
)

- Phys.Rev.Lett. 71 (1993) 666-669
•
e-Print:
- hep-th/9303048
•
DOI:
- 10.1103/PhysRevLett.71.666

[21]

Holographic Complexity

Mohsen Alishahiha
(
- IPM, Tehran
)

- Phys.Rev.D 92 (2015) 12, 126009
•
e-Print:
- 1509.06614
•
DOI:
- 10.1103/PhysRevD.92.126009

[22]

On Volumes of Subregions in Holography and Complexity

Omer Ben-Ami
(
- Tel Aviv U.
)
,
Dean Carmi
(
- Perimeter Inst. Theor. Phys. and
- Tel Aviv U.
)

- JHEP 11 (2016) 129
•
e-Print:
- 1609.02514
•
DOI:
- 10.1007/JHEP11(2016)129

[23]

The Gravity Dual of a Density Matrix

- Class.Quant.Grav. 29 (2012) 155009
•
e-Print:
- 1204.1330
•
DOI:
- 10.1088/0264-9381/29/15/155009

[24]

Causality & holographic entanglement entropy

Matthew Headrick
(
- Brandeis U.
)
,
Veronika E. Hubeny
(
- Durham U., CPT and
- Durham U., Dept. of Math.
)
,
Albion Lawrence
(
- Brandeis U.
)
,
Mukund Rangamani
(
- Durham U., CPT and
- Durham U., Dept. of Math.
)

- JHEP 12 (2014) 162
•
e-Print:
- 1408.6300
•
DOI:
- 10.1007/JHEP12(2014)162

[25]

Surface terms as counterterms in the AdS / CFT correspondence

Roberto Emparan
(
- Durham U., Dept. of Math. and
- Basque U., Bilbao
)
,
Clifford V. Johnson
(
- Kentucky U.
)
,
Robert C. Myers
(
- McGill U.
)

- Phys.Rev.D 60 (1999) 104001
•
e-Print:
- hep-th/9903238
•
DOI:
- 10.1103/PhysRevD.60.104001

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